Terms in Wave Motion

The respective displacements (in $\mathrm{cm}$) of the two particles are given by the equations:

$y_1=2\sin 3\pi t$

$y_2=2\sin \left(3\pi t-\frac{\pi }{8}\right)$

and these two particles of medium disturbed by the wave propagation are at $x_1=0$ and $x_2=1 \mathrm{cm}$, then wave speed is:

Two plane-progressive waves in the same phase must have:

Light waves travel in the form of _____waves.

Progressive waves are waves originating from a source such that they never return to the source.

On an average, a human heart is found to beat $72$ times a minute. Its frequency and period are

A point particle is acted upon by a restoring force $-k{x}^3.$ The time period of oscillation is $T$ when the amplitude is $A.$ The time period for an amplitude $2 A$ will be:

Monochromatic light of frequency $5\times {10}^{14} \mathrm{Hz}$ travelling in vacuum enters a medium of refractive index $1.5$. Its wavelength in the medium is

A point particle is acted upon by a restoring force $-k{x}^3.$ The time period of oscillation is $T$ when the amplitude is $A.$ The time period for an amplitude $2A$ will be:

Compare the velocities of the waveforms given below, and choose the correct option.

Two waves meet at a point. The waves have a path difference of $\frac{\lambda }{4}.$ The phase difference between the waves is

A particle of mass $\frac{2}{3} \mathrm{kg}$ with velocity $v=-15 \mathrm{m} {\mathrm{s}}^{-1}$ at $t=-2 \mathrm{s}$ is acted upon by a force $F=k-\beta t^2$. Here, $k=8 \mathrm{N}$ and $\beta =2 \mathrm{N} {\mathrm{s}}^{-2}$. The motion is one-dimensional. Then, the speed at which the particle acceleration is zero again, is

A ball is moving uniformly in a circular path of radius $1 \mathrm{m}$ with a time period of $1.5 \mathrm{s}$. If the ball is suddenly stopped at $t=8.3 \mathrm{s},$ the magnitude of the displacement of the ball with respect to its position at $t=0 \mathrm{s}$ is closest to:

The frequency of tuning fork is $500 \mathrm{Hz}$ and the velocity of sound in air is $300 \mathrm{m} {\mathrm{s}}^{-1}$. The distance travelled by sound while the fork executes $100$oscillations per second is ______.

Transverse waves are generated in two uniform wires $A$ and $B$ of the same material by attaching their free ends to a vibrating source of frequency $200 \mathrm{Hz}$. The cross-sectional area of $A$ is half that of $B$ while the tension on $A$ is twice that on $B$. The ratio of the wavelengths of the transverse waves in $A$ and $B$ is :

A wire of variable mass per unit length $\mathrm{\mu }={\mathrm{\mu }}_0\mathrm{x},$ is hanging from the ceiling as shown in figure. The length of wire is ${\mathrm{\ell }}_0$. A small transverse disturbance is produced at its lower end. Find the time after which the disturbance will reach to the other ends.

A pulse on a string is shown in the figure. $\mathrm{P}$ is particle of the string. Then state which of the following is incorrect.

Two sinusoidal waves with same wavelengths and amplitudes travel in opposite directions along a string with a speed $10 {\mathrm{ms}}^{-1}.$ If the minimum time interval between two instants when the string is flat is $0.5 \mathrm{s},$ the wavelength of the waves is

For the next two questions

Angular frequency in SHM is given by $\text{ω}=\sqrt{\frac{\text{k}}{\text{m}}}$. Maximum acceleration in SHM is ${\text{ω}}^{2}A$ and maximum value of friction between two bodies in contact is $\text{μ}\text{N}$, where N is the normal reaction between the bodies.

What will be the speed of the transverse wave in a $2.5 \mathrm{m}$ long rope hanging from the ceiling at the upper end and at a point $0.5 \mathrm{m}$ distance from the lower end respectively? Given the mass of the rope is $0.1 \mathrm{Kg}$ distributed uniformly.

Two steel wires $A$and $B$ are such that the diameter of $A$ is twice that of $B$ and the tension in $A$ is half of that in $B$. If transverse waves of same frequency are generated in both the wires, then compute the ratio of velocities of waves in $A$ and $B$.